[1]} provide an interesting Pareto-frontier entropy method as an acquisition function, and [2]} use Pareto-frontier heuristics to formulate new acquisition functions. Their approaches were not extended to mixed-variable problems because hyper-volume is difficult to define for combinatorial spaces. Hedge algorithms have proven to be efficient in dealing with a diverse set of problems. They use a portfolio of acquisition functions [3]}. However, these algorithms have not been considered for MOBO, and, to the authors' knowledge, there is no existing BO implementation that solves mixed-variable multi-objective problems.
